An analog ultrasonic pulsed phase locked loop (PPLL) has demonstrated parts-in-ten million resolution for measuring changes in the time of flight of an ultrasonic tone-burst. Analog ultrasonic pulsed phase locked loops have been used in diverse applications such as determining the load state of a fastener, measuring residual stress and nonlinear elastic constants, measuring intracranial and intramuscular pressure, measuring groundwater flows, measuring changes in the temperature of a water bath, and others.
The analog PPLL (APPLL) achieves its high resolution with a feedback loop architecture that maintains a constant 90° phase difference between a transmitted ultrasonic pulse and a received echo of that pulse from a test sample, sometimes simply referred to as an echo. To maintain this phase difference, the analog PPLL detects the phase of a sampled region of the received echo pulse, and changes the frequency of the next transmitted pulse to maintain phase quadrature (i.e., a 90° phase difference) between that transmitted pulse and the echo sample. Under this quadrature phase difference condition, the frequency of the transmitted pulse must be a harmonic of the fundamental frequency of the transmitted pulse defined by the following relation:fm=mv/2l  (1)where fm is the mth harmonic of the fundamental resonance frequency, v is the speed of sound in the transmitting medium, and l is the one-way propagation distance from the transmitter to sample under test. Equation (1) defines a resonance condition which is used to convert the frequency output of the APPLL into the speed of sound v or the ultrasonic path length l. These two parameters, v and l, may then be used to assess certain material properties of an object under test, such as elasticity, temperature or density.
In an analog PPLL, a phase detector estimates the phase of a received echo pulse, (usually a set of echo pulses), and feeds this received echo signal back to a voltage-controlled signal generator. If the echo signal phase is not in quadrature with the transmitted pulse signal, the signal generator shifts the frequency of the next transmitted pulse so that the resonance condition is met. The “loop” includes the pulse generator/transmitter (e.g., a voltage controlled oscillator), the echo pulse receiver, and the phase comparator or detector with the feedback of the phase difference to the pulse generator/transmitter.
The heart of the analog PPLL is an analog mixer that functions as the phase detector forming the product between the output reference signal V1=A1 sin(ω1+φ1) and the return echoes V2=A2(t)sin(ω2t+φ2), with A2(t) being a time-dependent function depending on the location of the various echoes. The output of the phase detector mixer, VM, is defined below:VM=½A1A2(t){cos [(ω1−ω2)t+(φ1−φ2)]+cos [(ω1−ω2)t+(φ1−φ2)]}  (2)In this application, the two frequencies are the same (ω1=ω2=ω) so equation (2) reduces to:VM=½A1A2(t){cos(Δφ)+cos(2ωt+(Σφ)}  (3)The 2ωt term is eliminated by applying a low-pass filter (coupled to the mixer output) to VM to yield a DC phase signal VP:VP=½A1A2(t)cos(Δφ)  (4)
Thus, the output of the filter depends on the amplitude of the transmitted pulse (i.e., the reference signal) and the received echo pulses as well as on the phase difference between the transmitted pulse and the received echo pulses. A sample-and-hold circuit (coupled to the filter's output) measures VP for a selected echo pulse, A2(t1), and the output of the sample-and-hold circuit is then sent to an integrator (which averages out pulse-to-pulse noise in VP). The integrator output h creates an error signal that is stabilized when Δφ=90°. For other values of Δφ, a “ramp” (either increasing or decreasing) error signal is returned to the VCO control voltage, which forces a frequency shift in the VCO output (the transmit pulse) to the resonance condition of equation (1).
APPLLs rely on analog components and analog-based phase estimation methods. For example, U.S. Pat. Nos. 4,363,242; 5,404,743; 5,214,955; and 4,624,142 employ analog signal processing components to measure phase, such as the mixer, low-pass filter, sample and hold circuit, and integrator as described above.
But these components are subject to thermal drift and other noise sources that limit the resolution of the APPLLs or the time over which a measurement must be taken. In addition, analog-based PPLLs can only estimate phase error rather than calculate the actual phase error, and they do not provide an accurate amplitude of the echo being tracked. That echo amplitude information can be very useful information. It is also difficult for APPLLs to accurately select an echo pulse and an optimal sampling region of that pulse.